package euler.p051_100;

import euler.MainEuler;

public class Euler075 extends MainEuler {

    /*
        It turns out that 12 cm is the smallest length of wire
        that can be bent to form an integer sided right angle
        triangle in exactly one way, but there are many more examples.

        12 cm: (3,4,5)
        24 cm: (6,8,10)
        30 cm: (5,12,13)
        36 cm: (9,12,15)
        40 cm: (8,15,17)
        48 cm: (12,16,20)

        In contrast, some lengths of wire, like 20 cm, cannot be bent
        to form an integer sided right angle triangle, and other lengths
        allow more than one solution to be found;
        for example, using 120 cm it is possible to form exactly three
        different integer sided right angle triangles.

        120 cm: (30,40,50), (20,48,52), (24,45,51)

        Given that L is the length of the wire, for how many values
        of L ≤ 1,500,000 can exactly one integer sided right angle
        triangle be formed?

     */

    // http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Pythag/pythag.html#mnformula
    public String resolve() {

        int limite = 1500000;

        int[] array = new int[limite+1];

        for (int m = 1; 2*m*(m+1) <= limite; m++) {
            for (int n = 1; (n < m) && (2*m*(m+n) <= limite); n++) {
                if (((m + n) % 2 == 1) && (primeHelper.MCD(m,n) == 1)) {
                    int p = 2*m*(m+n);

                    for (int i = p; i <= limite; i+=p) {
                        array[i]++;
                    }
                }
            }
        }

        int count = 0;
        for (int i = 0; i < array.length; i++) {
            if (array[i] == 1) {
                count++;
            }
        }

        return String.valueOf(count);
        // 161667
    }

}
